Abstract

The minimum weighted connected dominating set problem is a significant NP-hard problem with wide applications, and is an extension of the classical minimum dominating set problem. In order to solve this problem, we present a restart local search algorithm with tabu method (RLS$\_$ Tabu). In our RLS$\_$ Tabu algorithm, we firstly involve the random restart initialization method to jump out of the local optimum. Meanwhile, RLS$\_$ Tabu algorithm also applies tabu method in neighborhood search procedure to mitigate the cycling problem. Secondly, we present two strategies in neighborhood search procedure for removing vertices properly, which one is greedy and random strategy, and another one is multiple deletion strategy. The two strategies are crucial to improve the solution quality. Thirdly, the solution connected vertex is important to guarantee the feasibility of solutions. Therefore, we maintain the solution connected vertex set during the neighborhood search, and select the vertex to be added from this set. Finally, in order to intensify the solution, RLS$\_$ Tabu utilizes the pruning function to delete redundant vertices in the candidate solution. In experimental section, we will compare our algorithm with the other six algorithms on three types of benchmarks. Experimental results indicate that our algorithm significantly outperforms the comparative algorithms on most benchmark instances.

摘要

最小加权连通支配集问题是具有广泛应用的重要NP-hard问题，是经典最小支配集问题的扩展。为了解决这个问题，我们提出了一种带有禁忌方法的重启局部搜索算法（RLS$\_$禁忌）。在我们的 RLS$\_$禁忌算法，我们首先涉及随机重启初始化方法以跳出局部最优。同时，RLS$\_$禁忌算法还在邻域搜索过程中应用禁忌方法来缓解循环问题。其次，我们在邻域搜索过程中提出了两种正确删除顶点的策略，一种是贪婪随机策略，另一种是多重删除策略。这两种策略对于提高解决方案质量至关重要。第三，解连通顶点对于保证解的可行性很重要。因此，我们在邻域搜索过程中维护解连通顶点集，并从该集合中选择要添加的顶点。最后，为了强化解，RLS$\_$Tabu 利用剪枝功能删除候选解中的冗余顶点。在实验部分，我们将在三种基准上将我们的算法与其他六种算法进行比较。实验结果表明，我们的算法在大多数基准实例上明显优于比较算法。